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21B-B11.M1P

# 21B-B11.M1P - y = 0 y = 4 x-x 2 and y = 4-x 2(Hint It might...

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Math 21B section B Winter 2011 Practice Midterm 1. Please do not use any notes, calculators or books. 1. (10 points) Velocity is measured every 2 minutes and given in the following table: time in minutes 0 2 4 6 velocity in miles per minute 11 10 8 7 (a) Estimate the number of miles traveled in the 6 minutes. (b) If the velocity is decreasing, is the estimate you found an upper or lower bound on the actual distance traveled? 2. (10 points) At t hours after midnight a levee leaks at a rate of R ( t ) = π cos( π 24 t ) + 3 arce-feet of water per hour. (The periodicity is due to tides and acre-feet are units of volume). How much water leaked between 4:00 and 12:00? 3. (15 points) Consider the region in the Frst quadrant bounded by

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Unformatted text preview: y = 0, y = 4 x-x 2 and y = 4-x 2 . (Hint: It might help to sketch the region, which is roughly triangular with one corner at the point (1 , 3)). (a) ±ind the area of the region. (b) ±ind the volume of the solid obtained by rotating the region about the x-axis. (c) ±ind the volume of the solid obtained by rotating the region about the y-axis. 4. (10 points) ±ind the following numbers: (a) i x =1 x =-1 x 3 r x 4 + 1 dx = (b) i x =5 x = e dx x ln( x ) = 5. (15 points) ±ind the following functions: (a) i cos(3 x ) (5 sin(3 x ) + 7) 2 dx = (b) i sin( e 2 x ) e 2 x dx = (c) d dx i 2 x 1 cos 2 ( t 4 ) dt =...
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21B-B11.M1P - y = 0 y = 4 x-x 2 and y = 4-x 2(Hint It might...

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